Important quantities for solidification phenomena are the latent
heat of fusion [1]}, [2]} as well as the densities
of the solid and liquid phases at the melting temperature \(T_M\) .
Its determination requires the calculation of the enthalpy difference
between the liquid and solid branches at the melting temperature
\(T_M\) . The temperature evolution of the enthalpy at ambient pressure
for the solid and liquid branches of the HDNN potential are drawn
in Fig. REF . The simulation is started with a perfect fcc
crystal at \(T=300\)  K and heated stepwise with a temperature step
of 50 K with an average heating rate of \(10^{12}\)  K/s. At each
temperature, a simulation is performed over 50 ps (25 ps
equilibration and 25 ps production) during which an average value
of the enthalpy is calculated. The increase of temperature is
repeated until a dynamic melting is observed, that occurred at
\(T=1250\)  K. The latter value is noticeably higher than the thermodynamic
melting temperature \(T_M=970\)  K obtained from LSI simulations due
to overheating effects. For the liquid branch, the simulations are
started at \(T=1600\)  K with an equilibrated configuration after the
heating process. The same procedure as for the solid branch is
followed but with a step-wise cooling down to 300 K that we called
the slow cooling. Above \(T=1250\)  K, the difference in the enthalpy
from the heating and cooling processes is negligible, indicating
that there is no reminiscence of the crystalline state. Below 600 K
the liquid undergoes a partial crystallization during cooling.
Then, the cooling procedure for the liquid branch is repeated with
a higher cooling rate of \(10^{13}\)  K/s to avoid crystallization,
and a glass transition is seen at \(T_G=378\)  K inferred from a
crossover between the liquid and glassy branches as shown in
Fig. REF . From the liquid and solid branches we find an enthalpy
of melting of \(11.67\)  kJ/mol which compares reasonably well with
the experimental value of \(13.34\)  kJ/mol [3]}. Taking
the numerical derivative of the solid branch yields a value of the
specific heat at constant pressure, \(C_P\) , of \(0.99\)  J/g/K which
is also in good agreement with the experimental value of \(0.91\)  J/g/K.
For the liquid a value of \(1.158\)  J/g/K is obtained, which is in
the range of experimental data between \(1.03\)  J/g/K and \(1.18\)  J/g/K
close to the latest assessed values of \(1.127\)  J/g/K [3]}.
The specific heat is a typical derivative quantity that depends on
the fluctuations of the enthalpy [5]}, [6]}. The very
good agreement is a strong indication that including the time
fluctuations from AIMD is a fruitful strategy to describe at least
the thermodynamics.
